Abstract The many complex regions of positive and negative flux that thread the surface of the Sun are mainly grouped around the edges of supergranule cells. These cells have large concentrations of magnetic flux on their boundaries and very little flux inside, with the magnetic fragments that appear in the centre of the cells swept to the boundaries by convective motions. Thus, a small bipolar pair of magnetic fragments (such as an ephemeral region) emerges inside a cell and moves towards the cell boundary as it grows. On reaching the boundary the fragments encounter unipolar regions of network flux with which they may merge or cancel. When cancellation takes place there is often an associated X-ray bright point in the overlying corona. Here, the emergence and interaction of an ephemeral region in a quiet-region or active-region super-granule cell is considered. It is found that there are three possible scenarios for the evolution of an ephemeral region in a supergranule cell and these are all investigated. The magnetic fields for the supergranule cell and ephemeral region are modelled by finite sources of flux and are studied as the ephemeral region moves through a series of quasi-static states. It is found that the ratio of the cancelling fragment widths (strengths) is important in determining the lifetime and path of the bright point, while the actual sizes of the fragments is important for determining the intensity of the bright point, the lifetime of the cancelling magnetic feature and the relative times of the bright point completion and cancelling magnetic feature onset. From this we suggest that transient brightenings in active regions and bright points on the quiet Sun may both be created by the converging flux mechanism detailed here.
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